Question: 3 people can paint 7 walls in 34 minutes. How many minutes will it take for 10 people to paint 9 walls? Round to the nearest minute.
Solution: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 3\text{ people}\\ t &= 34\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{34 \cdot 3} = \dfrac{7}{102}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 9 walls with 10 people. $t = \dfrac{w}{r \cdot p} = \dfrac{9}{\dfrac{7}{102} \cdot 10} = \dfrac{9}{\dfrac{35}{51}} = \dfrac{459}{35}\text{ minutes}$ $= 13 \dfrac{4}{35}\text{ minutes}$ Round to the nearest minute: $t = 13\text{ minutes}$